Question: Gabriela is 8 years older than Omar. Two years ago, Gabriela was 5 times as old as Omar. How old is Gabriela now?
Explanation: We can use the given information to write down two equations that describe the ages of Gabriela and Omar. Let Gabriela's current age be $g$ and Omar's current age be $o$ The information in the first sentence can be expressed in the following equation: $g = o + 8$ Two years ago, Gabriela was $g - 2$ years old, and Omar was $o - 2$ years old. The information in the second sentence can be expressed in the following equation: $g - 2 = 5(o - 2)$ Now we have two independent equations, and we can solve for our two unknowns. Because we are looking for $g$ , it might be easiest to solve our first equation for $o$ and substitute it into our second equation. Solving our first equation for $o$ , we get: $o = g - 8$ . Substituting this into our second equation, we get the equation: $g - 2 = 5($ $(g - 8)$ $ -$ $ 2)$ which combines the information about $g$ from both of our original equations. Simplifying the right side of this equation, we get: $g - 2 = 5g - 50$ Solving for $g$ , we get: $4 g = 48$ $g = 12$.